Affiliation:
1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
2. Department of Mathematics, Changsha University of Science and Technology, Changsha 410076, China
Abstract
We prove that the functionfα,β(x)=Γβ(x+α)/xαΓ(βx)is strictly logarithmically completely monotonic on(0,∞)if(α,β)∈{( α,β):1/α≤β≤1, α≠1}∪{(α,β):0<β≤1,φ1(α,β)≥0,φ2(α,β)≥0}and[fα,β(x)]-1is strictly logarithmically completely monotonic on(0,∞)if(α,β)∈{(α,β):0<α≤1/2,0<β≤1}∪{(α,β):1≤β≤1/α≤2,α≠1}∪{(α,β):1/2≤α<1,β≥1/(1-α)}, whereφ1(α,β)=(α2+α-1)β2+(2α2-3α+1)β-αandφ2(α,β)=(α-1)β2+(2α2-5α+2)β-1.
Funder
China-funded Postgraduates Studying Aboard Program for Building Top University
Subject
Applied Mathematics,Analysis